{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T08:52:43Z","timestamp":1649148763943},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p> Partition of G into edge-disjoint H-factors is called H-factorization of G. Muthusamy and Paulraja have conjectured that for k \u2265 3, K<jats:sub>m<\/jats:sub>\u25a1K<jats:sub>n<\/jats:sub> has a P<jats:sub>k<\/jats:sub>-factorization if and only if mn \u2261 0 ( mod k) and k(m + n - 2) \u2261 0 ( mod 2(k - 1)), where \u25a1 denote cartesian product of graphs. In this paper, it is shown that the necessary conditions mn \u2261 0 ( mod 5) and 5(m + 1) \u2261 0 ( mod 8) are sufficient for the existence of a P<jats:sub>5<\/jats:sub>-factorization of K<jats:sub>m<\/jats:sub>\u25a1C<jats:sub>n<\/jats:sub> when <\/jats:p><jats:p> (i) m = 7, n \u2261 0 ( mod 5), <\/jats:p><jats:p> (ii) m \u2261 175 ( mod 280), n \u2261 0( mod 5). <\/jats:p><jats:p> Further, it is shown that the necessary conditions mn \u2261 0 ( mod 5) and 5(m + n - 2) \u2261 0 ( mod 8) are sufficient for the existence of a P<jats:sub>5<\/jats:sub>-factorization of K<jats:sub>m<\/jats:sub>\u25a1K<jats:sub>n<\/jats:sub> in the following cases: <\/jats:p><jats:p> (i) m \u2261 5 ( mod 40), n \u2261 5 ( mod 40), <\/jats:p><jats:p> (ii) m \u2261 10 ( mod 40), n \u2261 0 ( mod 40), <\/jats:p><jats:p> (iii) m \u2261 15 ( mod 120), n = 3 and m \u2261 15 ( mod 120), n \u2261 75 ( mod 120), <\/jats:p><jats:p> (iv) m \u2261 20 ( mod 40), n \u2261 30 ( mod 120), <\/jats:p><jats:p> (v) m \u2261 25 ( mod 40), n \u2261 25 ( mod 40), <\/jats:p><jats:p> (vi) m \u2261 30 ( mod 120), n = 4 and m \u2261 30 ( mod 120), n \u2261 20 ( mod 40), <\/jats:p><jats:p> (vii) m \u2261 75 ( mod 120), n \u2261 15 ( mod 120), <\/jats:p><jats:p> (viii) m \u2261 0 ( mod 40), n = 2 and m \u2261 0 ( mod 40), n \u2261 10 ( mod 40). <\/jats:p><jats:p> In fact our results partially answer the above conjecture when k = 5. <\/jats:p>","DOI":"10.1142\/s1793830914500190","type":"journal-article","created":{"date-parts":[[2014,1,16]],"date-time":"2014-01-16T22:38:38Z","timestamp":1389911918000},"page":"1450019","source":"Crossref","is-referenced-by-count":2,"title":["P<sub>5<\/sub>-FACTORIZATION OF CARTESIAN PRODUCT OF GRAPHS"],"prefix":"10.1142","volume":"06","author":[{"given":"A.","family":"TAMIL ELAKKIYA","sequence":"first","affiliation":[{"name":"Department of Mathematics, Periyar University, Salem, TamilNadu, India"}]},{"given":"A.","family":"MUTHUSAMY","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Periyar University, Salem, TamilNadu, India"}]}],"member":"219","published-online":{"date-parts":[[2014,3,19]]},"reference":[{"key":"rf1","first-page":"60","volume":"63","author":"Chitra V.","journal-title":"Bull. Inst. Combin. Appl."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-006-0289-0"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00176-9"},{"key":"rf5","first-page":"127","volume":"84","author":"SampathKumar R.","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90227-0"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788695"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.09.046"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90305-D"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:44:19Z","timestamp":1565178259000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,19]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,3,19]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S1793830914500190"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500190","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,19]]}}}